“Doppler” Ultrasound Misnomer or Misunderstood?

Current (board) exam review materials for medical imaging professionals include questions that explicitly refer to the Doppler shift equation and computation of the resulting frequency shift (eg, Nickoloff1 and Abrahams2). They cite textbooks and other reference materials that also refer to the Doppler shift equation and portray its use as the physical principle for flow visualization on clinical ultrasound scanners. However, the Doppler shift principle is actually used infrequently and only for specific applications. As such, the mechanisms for ultrasound-based flow visualization should be clarified (Figure 1). “Doppler” is a ubiquitous imaging mode available on virtually all clinical ultrasound devices. Traditionally, 3 specific modes are implemented: (a) pulse wave mode (PW), also known as spectral Doppler; (b) color flow mode (CF), also known as color Doppler (referring to both color velocity and color power); and (c) continuous wave mode (CW). In addition, there are specialized flow modes such as super-resolution for microvascular visualization, tissue Doppler, and others. Note that ultrasound imaging is almost entirely based on pulse-echo depth information, that is, the time between pulse transmission and echo reception. A system with continuous transmission does not allow for imaging that relies on pulse-echo depth determination and is therefore not capable of creating an image. Gated (imaging) systems briefly open a “gate” to allow transmission of an ultrasound pulse. This transmit gate is then closed, and a receive gate is opened to enable echo reception and allow for “pulse-echo” sampling (eg, imaging). From a device implementation standpoint, there are 2 categories of flow modes: continuous (CW) and gated-imaging (PW, CF) systems. There is a class of techniques called zero-crossing indicators.3, 4 These techniques can determine when the waveform from a received acoustic wave (ie, echo) crosses 0 volts (which denotes 0 pressure). This can be expanded to tracking multiple zero-crossings, either from an echo generated by 1 pulse (“intra-pulse”) or from echoes generated by multiple pulses (“inter-pulse”). Intra-pulse tracking identifies the zero-crossings of a single waveform for frequency estimation, which can then be used to calculate a Doppler shift. However, this shift is typically too small to measure on a gated system due to the limited frequency resolution of gated systems. Inter-pulse tracking identifies the zero-crossings between successive pulse echoes, that is, the pair of red pulses in Figure 2, which are generated by transmits at a set pulse repetition frequency (PRF). The lower the PRF, the more blood cells have moved between the current pulse-echo transmit and the previous transmission. In other words, the phase shift becomes measurable. That is what is being measured in current ultrasound scanners, except that there are better methods to obtain zero-crossings, such as correlators and Fourier transforms. But it is the same concept: assessing the shift in phase across echoes from successive transmit pulses. The maximum allowable phase shift is ±180° (or ±π, or plus/minus period length T of the ultrasound pulse); otherwise, one faces aliasing. By adjusting the PRF, one can tune the magnitude of the resulting phase shift, that is, how much of the velocity range is being used. Figure 2 illustrates both intra-pulse estimates, that is, true Doppler frequency shift data, as well as inter-pulse estimates of arrival times, both based on the zero-crossing of the rising phase. The first documented use of a gated Doppler system (based on a CW device) was reported by Baker.10 Among others, Wells11 demonstrated the use of pulsed Doppler for potential cardiac applications. For a dual-element, 2-MHz, transmit/receive system, a maximum PRF of 1 kHz allowed for up to a 500-Hz Doppler shift, which corresponds to a maximum velocity of 15 cm/s at 𝛾 = 0°. Gated systems provide depth information, which is not available from CW systems. However, Wells' setup only offered sparse temporal sampling—with ~50-μs windows every 1 ms—and had therefore only limited spectral resolution, yet it allowed for real-time sampling of the cardiac cycle. Switzer and Nanda12 discussed the clinical need for 2D depiction of blood flow with an increased velocity range. At that time, maximum detectable velocities for gated systems were lower than the clinically relevant range, while both CW and gated systems were confined to a single image line (ie, an “A line”). As such, ultrasound contrast agents became a potential alternative for flow visualization as they are amenable to 2D imaging. The above-mentioned microvascular imaging is currently a frequently recognized modality which relies on long “packet size” (ie, the number of temporal samples used to estimate the phase shift) and advanced tissue clutter filtering techniques to boost the sensitivity of ultrasound to small vessels with slow blood flow. Since these techniques are essentially using Color Flow signals (ie, signal phase shift), they are also independent of the Doppler-induced frequency shift. In the literature, many flow imaging modes labeled as “Doppler” are actually based on phase shift estimation. Cobbold13 stated that pulsed systems seem to be inappropriately using Doppler's name. Thomas and Leeman (1991) also pointed out that most “devices do not use the Doppler effect directly,” noting that velocities based on zero-crossing detectors are “difficult to measure, due to the small size of the frequency shift.” In summary, the Doppler shift plays only a minor role in pulsed systems, which instead rely on an inter-pulse phase shift for velocity estimation (Jensen 1996). *Color Flow can specify the display of velocity or power and thus be called CF velocity or CF power. Second, (board) exams should only ask for the computation of Doppler shift frequencies in connection with CW mode. For PW and CF, board exams should ask for the computation of the resulting phase shift, as it would illustrate the occurrence of aliasing for cases where the PRF is too low. Moreover, the computation would also illustrate that lowering the transmit frequency could potentially remedy cases of aliasing. Doppler as a conceptual method is easily understood by most as we experience Doppler shifts in everyday life. Visualizing flow can either be based on a signal frequency shift (ie, Doppler effect) or phase shift. It is therefore insightful to understand the Doppler effect in the context of phase, which denotes a signal's relative position (ie, from 0 to 2π) within its periodic cycle.13, 14 Because frequency is inversely proportional to a cycle's period, an increase (or decrease) in frequency due to the Doppler effect results in a decrease (or increase) in intra-signal phase. Consequently, the phase of a pulse-echo signal from stationary soft tissue is steady, whereas the phase of an echo signal from within the bloodstream rapidly changes due to the blood's motion. Repeated pulse-echo interrogation of the same region of interest allows for measurement of inter-signal phase changes, which can be used to determine local flow velocity.15, 16 Originally, analog zero-crossing circuits16-18 were implemented to visualize flow by providing timing information regarding when RF waveforms changed polarity (ie, “crossed zero”). Such timing can be used for phase tracking as well as to derive Doppler measurements. Intra-signal waveform zero-crossings yield the frequency shift of a moving target, while inter-signal zero-crossings provide the echo phase changes of repeated pulses from a target. Extracting the Doppler frequency shift of a moving red blood cell can be accomplished by analysis of the Fourier transform of the backscattered RF waveform (Figure 3). Figure 4 shows a simulation example of a stationary/reference waveform (—) as well as a Doppler-shifted waveform (........) due to a motion of 50 cm/s. A short tone burst is used for adequate spatial resolution. In this example, a 5-cycle, 3.75-MHz excitation provides a 2.5-μs temporal and 1.03 mm spatial resolution. However, there is not enough spectral resolution to observe the underlying Doppler frequency shift of 1.2 kHz (see middle panel in Figure 4). When increasing the number of cycles to 7500, a frequency resolution of 500 Hz is achieved, which allows for a 1.2-kHz Doppler frequency shift to be sampled, yielding an estimated velocity of 41 cm/s. However, such a long waveform (spanning more than 11 meters!) fails to provide clinical spatial resolution as it approximates a CW transmit. Instead of deriving the scatterer velocity from a Doppler shift of the waveform's center frequency, one can evaluate the amplitude or complex phase φ of samples obtained from repeated range-gate samples, as shown in Figure 5. For times T1, …, TN, the RF phase is recorded at the PRF rate, that is, PRF = 1/(Tn − Tn−1). A Fourier transform of the phase function, ɸ(f) = FT(φ(T)), yields the spectral component shown in the PW Doppler display; this is not the Doppler frequency shift but is rather the rate of change of the signal phase. Figure 6 presents a simulation-based example whereby the complex phase of a packet of N firings is interrogated at the center of the tone burst. For a packet length of 8 firings, the spectral resolution is very limited (1.4 kHz), as seen in the middle panel. However, an increase to 128 firings provides a 100-Hz spectral resolution, which is sufficient to resolve the 1.2-kHz shift caused by the moving scatterer. Note that the phase change due to displacement of the scatterer from firing to firing is the dominant (and accumulating) variable. Since the PRF is ~1000× lower than the carrier frequency, the pulse-echo phase shift is ~1000× larger than the frequency shift due to Doppler effect. In summary, the Doppler effect causes an intra-pulse phase shift, whereas the scatterer motion sampled at the PRF causes an inter-pulse phase shift, which is significantly larger than the former and can be tuned by adjusting the PRF. Figure 7 (left) shows the acquired RF data for a CF sequence with 16 firings. The abscissa is the fast-time axis of the individual receive data, while the ordinate axis depicts slow time, dictated by the PRF. Velocity estimation is shown across the range of CF power larger than 10% of the observed maximum, yielding an average velocity error of 1.4%. Actual implementations could utilize only the central portion of the estimates—where the average error is only 0.12%—since the waveforms overlap for all firings. It is well known that CF aliases when color velocities v exceed the current maximum velocity vNy, that is, either v > vNy or v < -vNy. Aliasing occurs when the phase change ∆ φ i $$ \Delta {\varphi}_i $$ between 2 adjacent firings exceeds ±π, that is, ∆ φ i > π $$ \Delta {\varphi}_i>\pi $$ or ∆ φ i ≤ − π $$ \Delta {\varphi}_i\le -\pi $$ . As one can see from Equation (1), df does not alias. As such, CW waveforms do not alias since they are based on the actual Doppler frequency shift df. As shown previously, Doppler frequency shifts are generally small compared to their transmit frequency fo. The sensitivity of phase changes, however, can be optimized since the PRF can be lowered until a large enough phase shift is present. Unfortunately, phase shifts encountered in clinical applications are often too large and cause aliasing. As such, one might consider a hybrid approach where small velocities are derived from phase shifts and large velocities from the actual Doppler shift. Ultrasound is subject to frequency-dependent attenuation. Waveforms emitted with a center frequency fc are received at fr < fc due to the preferential attenuation of higher frequencies, which causes a downshift of a waveform's frequency content. Ultrasonic transmit pulses are finite in the time domain and are therefore composed of a finite frequency spectrum ranging from fmin to fmax. Example: A CF pulse with a center frequency of fc = 5 MHz will experience a center frequency shift of −300 kHz when penetrating L = 2 × 3 cm (ie, round trip) of tissue with an acoustic attenuation α = 0.5 dB/MHz/cm, a(L) = a(0)·e−α·f·L, as derived from the center frequency shift of an echo returning from 3 cm in a Field II simulation with and without acoustic attenuation. This shift is much larger than the Doppler shift and will thus shadow the measured flow velocity, when acquired by using the Doppler property. Narrowband emissions (eg, CW) are not subject to frequency shifts since they (approximately) only possess 1 frequency (fo). While the amplitude of this waveform will decrease due to attenuation, there will be no center frequency shift since the transmission has no frequency range, that is, fc = fmin = fmax. Such a waveform will therefore be able to accurately assess velocities based on resulting Doppler frequency shifts. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.